Hmmm... not sure exactly how much CPU power you need. A more manageable analog filter might have a bandwidth of 10-20%, in which case you need a sample rate only modestly higher than the center frequency itself. For which a SAMD21 might actually have enough sample rate out of the box, but you may consider an external ADC for better performance as well.
You'd then need, let's see... you'll want a digital filter to start off, with modest bandwidth, to clean up the band skirts left from the analog filter; this might be a couple IIR filters needing say 4-16 MAC operations. You want to downconvert (decimate or mix) at some point, which should take a few more MACs and such. I don't know the exact performance of the SAMD21 but typical ARMs at 100MHz or thereabouts ought to be enough for that, or a little marginal, in which case a more DSP-tuned architecture, or higher clock, would do.
Once it's converted down, you can demodulate directly (direct conversion, implemented digitally), or keep it at a modest center frequency and continue filtering and stuff. Eventually I guess you'll be demodulating it in whatever way; if that requires a 90 degree phase shift (Hilbert transform), or FFT, you'll probably want something beefier.
You will want to have the ADC output buffered I think, so the DSP operations can be done in blocks. Interrupt per sample might not be too bad, but it does bring in a fair amount of overhead, and you don't have too much time to spend before the next sample comes in.
If you can reduce the bandwidth at any earlier point, you can of course get by with less CPU power. A signal of just a few kHz bandwidth could even be handled by an Arduino or PIC, a Cortex M0+ is definitely overkill compared to the minimum possible processing (but, that would require a faster sample-and-hold than an Arduino's ADC can do, and a much tighter analog filter which doesn't save you from the OP problem
).
I'm not an expert on digital radio systems, and it may be there are better optimizations. If nothing else, you can write out the signal chain in exactly the same way you'd solve it analog, then implement the difference functions to solve them in DSP. That's kind of where I'm approaching this from.
Tim